**HP 17BII and HP 17BII+: Sales Tax, Substantial Presence Test, Automobile Purchase, Principal Interest Property Tax & Insurance (PITI), Retirement Accounts**

Note: Some equations have the L (Let) and G (Get) functions, which are not available on the brown keyboard of the 17BII+ (around 2003).

**Sales Tax: Determine the total amount of taxable items and non-taxable items.**

AMT=NTAX+TXBL*(1+R%÷100)

AMT: Total Amount

NTAX: Items not subject to sales tax

TXBL: Items subject to sales tax

R%: sales tax rate

Example 1: A company purchases equipment which costs $99.99, which was subject to 9.5% sales tax, which includes $139.99 of services. The services are not subject to sales tax. What is the total invoice?

Input:

NTAX: 139.99

TXBL: 99.99

R%: 9.5(%)

Output:

AMT = 249.48

The total of the invoice is $249.48.

Example 2: During an audit, a company finds an invoice with the total of $236.40 (amount), and the invoice listed non-taxable services of $146.50. The company lives in a county where the sales tax is 8.75%. What is the amount of taxable items?

Input:

NTAX: 146.50

R%: 8.75(%)

AMT: 236.40

Output:

TXBL = 82.67

The amount of taxable items on the invoice is $82.67.

**Substantial Presence Test**

For more information about the substantial presence test, please click here: http://edspi31415.blogspot.com/search?q=substantial+presence+

This equation uses Let and Get.

SPT=IF(L(X:DDAYS(D:12.31+FP(100*D)÷100:1)>183:DATE(D:183):DATE(1.01+(FP(100*D)+.0001)÷100:IP(183-G(X)÷3)))

STP: Number of days calculated for the Substantial Presence Test

D: Date (in the format DD.MMYYYY)

Example 1:

D: 1.052019 (1/5/2019), SPT = 7.072019 (7/7/2019)

Example 2:

D: 6.182008 (6/18/2008), SPT = 12.182008 (12/18/2008)

Example 3:

D: 9.262018 (9/26/2018), SPT = 6.012019 (6/1/2019)

Example 4:

D: 7.102017 (7/10/2017), SPT = 5.062018 (5/6/2018)

**Financing the Purchase of an Automobile**

This equation deals with the purchase of an automobile.

AUTO:PRICE*(1-DISC%*.01)*(1+STAX%*.01)-DOWN=PMT*USPV(I%÷12:YRS*12)

PRICE: Sticker price of the automobile

DISC%: Discount percent

STAX%: Sales tax rate

DOWN: Down payment (amount)

PMT: Payment of the loan

I%: Interest rate of the loan

YRS: Number of years of the loan

Example 1: The sticker price of a car is $28,000.00. A discount of 15% is offered. The car is subject to 10% sales tax. The dealer offers a 6-year loan at 4.5%. With $2,000, what is the monthly payment?

Input:

PRICE: 28000.00

DISC%: 15

STAX%: 10

DOWN: 2000

I%: 4.5

YRS: 6

Output:

PMT = 383.83

The monthly payment is $383.83.

Example 2: Assuming the same facts from Example 1, expect the buyer wants to pay no more than $350.00 a month. What is the required down payment?

Input:

PRICE: 28000.00

DISC%: 15

STAX%: 10

I%: 4.5

YRS: 6

PMT: 350.00

Output:

DOWN = 4131.42

The down payment needs to be $4,131.42.

**Real Estate: Principal Interest Property Tax & Insurance (PITI)**

Determine the total payment of mortgage when considering property tax and property insurance.

PITI=MORT÷USPV(I%÷12:YRS*12)+(PROP$+INS$)÷12

PITI: Payment including principal, interest, property tax, and insurance

MORT: Mortgage amount, price of the property

I%: Annual interest rate

YRS: Number of the years of the mortgage

PROP$: Annual property tax

INS$: Annual property insurance

Example: A buyer purchases a home with a price of $200,000.00. The amount is to be financed. The loan lasts for 30 years and 5% interest rate. There is annual property tax of $1,200.00 with insurance of $395.95. What is the buyer's PITI?

Input:

MORT: 200000.00

I%: 5

YRS: 30

PROP$: 1200.00

INS$: 395.95

Output:

PITI = 1206.64

The buyer's PITI is $1,206.64.

**Retirement Accounts: Future Value and Earned Untaxed Dividends**

Determine the future value and untaxed dividends of tax-free retirement accounts (IRS/Keogh).

There are two versions, the second uses Let (L) and Get (G) functions.

Version 1:

IRA: VAL*0+DIV*0+IF(S(VAL):USFV(I%:YRS)*PMT*(1+I%÷100)-VAL:0)+IF(S(DIV):(USFV(I%:YRS)*(1+I%÷100)-YRS)*PMT-DIV:0)

Version 2:

IRA:(VAL+DIV+L(X:USFV(i%:YRS)*(1+I%÷100)))*0+IF(S(VAL):G(X)*PMT-VAL:(G(X)-YRS)*PMT-DIV)

Input Variables:

I%: Annual Interest Rate

YRS: Number of Years

PMT: Annual Payment

Output Variables:

VAL: Tax Free Value of the Retirement Account

DIV: Total Untaxed Dividends Earned

Remember, these are untaxed amounts.

Example:

I%: 6.88

PMT: 1000.00

YRS: 40

Output (Results):

VAL = 206811.01

DIV = 166881.01

Source:

Tony Hutchins, Luiz Vieria, and Gene Wright "HP 12C Platinum Solutions Handbook" Hewlett Packard. Revised 03.04 2004

Eddie

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